Pith Number

pith:5PTOI6ZQ

pith:2015:5PTOI6ZQLREHOE7TIZRL6N3TV5

not attested not anchored not stored refs pending

On tensor products of CSS Codes

Alain Couvreur, Benjamin Audoux

arxiv:1512.07081 v3 · 2015-12-22 · cs.IT · math.CO · math.IT · quant-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PTOI6ZQLREHOE7TIZRL6N3TV5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:05:00.865955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebe6e47b305c487713f34662bf3773af4001a5814923dbad53666299d3b3cfa8

Aliases

arxiv: 1512.07081 · arxiv_version: 1512.07081v3 · doi: 10.48550/arxiv.1512.07081 · pith_short_12: 5PTOI6ZQLREH · pith_short_16: 5PTOI6ZQLREHOE7T · pith_short_8: 5PTOI6ZQ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5PTOI6ZQLREHOE7TIZRL6N3TV5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ebe6e47b305c487713f34662bf3773af4001a5814923dbad53666299d3b3cfa8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2295279554d57af831e8d4ae853d80981fde664d0cc86a3178e37b9e60963ae1",
    "cross_cats_sorted": [
      "math.CO",
      "math.IT",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-12-22T13:37:23Z",
    "title_canon_sha256": "82da26868af0c242a673c57f880e1cf1d2ad79b592951f5f0217cfe3ce13770c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07081",
    "kind": "arxiv",
    "version": 3
  }
}